Week 5 BUS 308 assignment
RSaleemWeek 5 Correlation and Regression 
















 
For each question involving a statistical test below, list the null and alternate hypothesis statements. Use .05 for your significance level in making your decisions. 







 
For full credit, you need to also show the statistical outcomes  either the Excel test result or the calculations you performed. 









 




















1  Create a correlation table for the variables in our data set. (Use analysis ToolPak function Correlation.) 










 
 a. Interpret the results. What variables seem to be important in seeing if we pay males and females equally for equal work? 









 




















2  Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Mid, 









 
 age, ees, sr, raise, and deg variables.) (Note: since salary and compa are different ways of 











 
 expressing an employee’s salary, we do not want to have both used in the same regression.) 











 




















 Ho: The regression equation is not significant. 














 
 Ha: The regression equation is significant. 














 
 Ho: The regression coefficient for each variable is not significant 












 
 Ha: The regression coefficient for each variable is significant 












 




















 Sal 

 The analysis used Sal as the y (dependent variable) and 











 
 SUMMARY OUTPUT 
 mid, age, ees, sr, g, raise, and deg as the dependent 











 



 variables (entered as a range). 












 
 Regression Statistics 
















 
 Multiple R  0.99215498 

















 R Square  0.9843715 

















 Adjusted R Square  0.98176675 

















 Standard Error  2.59277631 

















 Observations  50 





































 ANOVA 



















 df  SS  MS  F  Significance F 













 Regression  7  17783.7  2540.52  377.914  8.44043E36 













 Residual  42  282.345  6.72249 















 Total  49  18066 





































 Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0% 










 Intercept  4.009  3.775  1.062  0.294  11.627  3.609  11.627  3.609 










 Mid  1.220  0.030  40.674  0.000  1.159  1.280  1.159  1.280 










 Age  0.029  0.067  0.439  0.663  0.105  0.164  0.105  0.164 










 EES  0.096  0.047  2.020  0.050  0.191  0.000  0.191  0.000 










 SR  0.074  0.084  0.876  0.386  0.244  0.096  0.244  0.096 










 G  2.552  0.847  3.012  0.004  0.842  4.261  0.842  4.261 










 Raise  0.834  0.643  1.299  0.201  0.462  2.131  0.462  2.131 










 Deg  1.002  0.744  1.347  0.185  0.500  2.504  0.500  2.504 






























Interpretation:  Do you reject or not reject the regression null hypothesis? 












 
 Do you reject or not reject the null hypothesis for each variable? 












 
 What is the regression equation, using only significant variables if any exist? 











 
 What does result tell us about equal pay for equal work for males and females? 











 








































3  Perform a regression analysis using compa as the dependent variable and the same independent 










 
 variables as used in question 2. Show the result, and interpret your findings by answering the same questions. 









 
 Note: be sure to include the appropriate hypothesis statements. 












 




















4  Based on all of your results to date, is gender a factor in the pay practices of this company? Why or why not? 









 
 Which is the best variable to use in analyzing pay practices  salary or compa? Why? 











 








































5  Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question? 




 
 What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? 








 

Score:  Week 5  Correlation and Regression  
<1 point>  1.  Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)  
a.  Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?  
b. Place table here (C8):  
c.  Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are  
significantly related to Salary?  
To compa?  
d.  Looking at the above correlations  both significant or not  are there any surprises by that I  
mean any relationships you expected to be meaningful and are not and viceversa?  
e.  Does this help us answer our equal pay for equal work question?  
<1 point>  2  Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint,  
age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of  
expressing an employee’s salary, we do not want to have both used in the same regression.)  
Plase interpret the findings.  
Ho: The regression equation is not significant.  
Ha: The regression equation is significant.  
Ho: The regression coefficient for each variable is not significant  Note: technically we have one for each input variable.  
Ha: The regression coefficient for each variable is significant  Listing it this way to save space. 

 
Sal  
SUMMARY OUTPUT  
Regression Statistics  
Multiple R  0.9915591  
R Square  0.9831894  
Adjusted R Square  0.9808437  
Standard Error  2.6575926  
Observations  50  
ANOVA  
 df  SS  MS  F  Significance F  
Regression  6  17762.3  2960.38  419.1516  1.812E36  
Residual  43  303.7003  7.0628  
Total  49  18066 


 
 Coefficients  Standard Error  t Stat  Pvalue  Lower 95%  Upper 95%  Lower 95.0%  Upper 95.0%  
Intercept  1.749621  3.618368  0.4835  0.631166  9.046755  5.5475126  9.04675504  5.54751262  
Midpoint  1.2167011  0.031902  38.1383  8.66E35  1.1523638  1.2810383  1.152363828  1.28103827  
Age  0.004628  0.065197  0.071  0.943739  0.136111  0.1268547  0.13611072  0.1268547  
Performace Rating  0.056596  0.034495  1.6407  0.108153  0.126162  0.0129695  0.12616237  0.01296949  
 Service  0.0425  0.084337  0.5039  0.616879  0.212582  0.1275814  0.21258209  0.12758138  
Gender  2.4203372  0.860844  2.81159  0.007397  0.6842792  4.1563952  0.684279192  4.15639523  
Degree  0.2755334  0.799802  0.3445  0.732148  1.337422  1.8884885  1.33742165  1.88848848  
Note: since Gender and Degree are expressed as 0 and 1, they are considered dummy variables and can be used in a multiple regression equation.  
Interpretation:  
For the Regression as a whole:  
What is the value of the F statistic:  
What is the pvalue associated with this value:  
Is the pvalue <0.05?  
Do you reject or not reject the null hypothesis:  
What does this decision mean for our equal pay question:  
For each of the coefficients:  Intercept  Midpoint  Age  Perf. Rat.  Service  Gender  Degree  
What is the coefficient's pvalue for each of the variables:  
Is the pvalue < 0.05?  
Do you reject or not reject each null hypothesis:  
What are the coefficients for the significant variables?  
Using only the significant variables, what is the equation?  Salary =  
Is gender a significant factor in salary:  
If so, who gets paid more with all other things being equal?  
How do we know?  
<1 point>  3  Perform a regression analysis using compa as the dependent variable and the same independent  
variables as used in question 2. Show the result, and interpret your findings by answering the same questions.  
Note: be sure to include the appropriate hypothesis statements.  
Regression hypotheses  
Ho:  
Ha:  
Coefficient hyhpotheses (one to stand for all the separate variables)  
Ho:  
Ha:  
Place D94 in output box.  
Interpretation:  
For the Regression as a whole:  
What is the value of the F statistic:  
What is the pvalue associated with this value:  
Is the pvalue < 0.05?  
Do you reject or not reject the null hypothesis:  
What does this decision mean for our equal pay question:  
For each of the coefficients:  Intercept  Midpoint  Age  Perf. Rat.  Service  Gender  Degree  
What is the coefficient's pvalue for each of the variables:  
Is the pvalue < 0.05?  
Do you reject or not reject each null hypothesis:  
What are the coefficients for the significant variables?  
Using only the significant variables, what is the equation?  Compa =  
Is gender a significant factor in compa:  
If so, who gets paid more with all other things being equal?  
How do we know?  
<1 point>  4  Based on all of your results to date,  
Do we have an answer to the question of are males and females paid equally for equal work?  
If so, which gender gets paid more?  
How do we know?  
Which is the best variable to use in analyzing pay practices  salary or compa? Why?  
What is most interesting or surprising about the results we got doing the analysis during the last 5 weeks?  
<2 points>  5  Why did the single factor tests and analysis (such as t and single factor ANOVA tests on salary equality) not provide a complete answer to our salary equality question?  
What outcomes in your life or work might benefit from a multiple regression examination rather than a simpler one variable test? 
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